/* Declarations for math functions.

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Copyright (C) 1991-2018 Free Software Foundation, Inc.

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This file is part of the GNU C Library.

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The GNU C Library is free software; you can redistribute it and/or

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modify it under the terms of the GNU Lesser General Public

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License as published by the Free Software Foundation; either

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version 2.1 of the License, or (at your option) any later version.

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The GNU C Library is distributed in the hope that it will be useful,

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but WITHOUT ANY WARRANTY; without even the implied warranty of

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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

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Lesser General Public License for more details.

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You should have received a copy of the GNU Lesser General Public

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License along with the GNU C Library; if not, see

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<http://www.gnu.org/licenses/>. */

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/*

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* ISO C99 Standard: 7.12 Mathematics <math.h>

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*/

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#ifndef _MATH_H

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#define _MATH_H 1

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#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION

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#include <bits/libc-header-start.h>

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#if defined log && defined __GNUC__

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# warning A macro called log was already defined when <math.h> was included.

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# warning This will cause compilation problems.

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#endif

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__BEGIN_DECLS

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/* Get definitions of __intmax_t and __uintmax_t. */

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#include <bits/types.h>

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/* Get machine-dependent vector math functions declarations. */

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#include <bits/math-vector.h>

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/* Gather machine dependent type support. */

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#include <bits/floatn.h>

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/* Value returned on overflow. With IEEE 754 floating point, this is

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+Infinity, otherwise the largest representable positive value. */

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#if __GNUC_PREREQ (3, 3)

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# define HUGE_VAL (__builtin_huge_val ())

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#else

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/* This may provoke compiler warnings, and may not be rounded to

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+Infinity in all IEEE 754 rounding modes, but is the best that can

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be done in ISO C while remaining a constant expression. 10,000 is

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greater than the maximum (decimal) exponent for all supported

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floating-point formats and widths. */

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# define HUGE_VAL 1e10000

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#endif

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#ifdef __USE_ISOC99

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# if __GNUC_PREREQ (3, 3)

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# define HUGE_VALF (__builtin_huge_valf ())

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# define HUGE_VALL (__builtin_huge_vall ())

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# else

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# define HUGE_VALF 1e10000f

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# define HUGE_VALL 1e10000L

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# endif

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#endif

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#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F16 (__builtin_huge_valf16 ())

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#endif

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#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F32 (__builtin_huge_valf32 ())

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#endif

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#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F64 (__builtin_huge_valf64 ())

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#endif

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#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F128 (__builtin_huge_valf128 ())

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#endif

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#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F32X (__builtin_huge_valf32x ())

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#endif

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#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F64X (__builtin_huge_valf64x ())

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#endif

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#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define HUGE_VAL_F128X (__builtin_huge_valf128x ())

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#endif

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#ifdef __USE_ISOC99

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/* IEEE positive infinity. */

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# if __GNUC_PREREQ (3, 3)

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# define INFINITY (__builtin_inff ())

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# else

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# define INFINITY HUGE_VALF

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# endif

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/* IEEE Not A Number. */

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# if __GNUC_PREREQ (3, 3)

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# define NAN (__builtin_nanf (""))

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# else

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/* This will raise an "invalid" exception outside static initializers,

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but is the best that can be done in ISO C while remaining a

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constant expression. */

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# define NAN (0.0f / 0.0f)

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# endif

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#endif /* __USE_ISOC99 */

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#if __GLIBC_USE (IEC_60559_BFP_EXT)

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/* Signaling NaN macros, if supported. */

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# if __GNUC_PREREQ (3, 3)

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# define SNANF (__builtin_nansf (""))

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# define SNAN (__builtin_nans (""))

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# define SNANL (__builtin_nansl (""))

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# endif

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#endif

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#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF16 (__builtin_nansf16 (""))

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#endif

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#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF32 (__builtin_nansf32 (""))

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#endif

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#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF64 (__builtin_nansf64 (""))

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#endif

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#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF128 (__builtin_nansf128 (""))

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#endif

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#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF32X (__builtin_nansf32x (""))

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#endif

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#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF64X (__builtin_nansf64x (""))

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#endif

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#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)

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# define SNANF128X (__builtin_nansf128x (""))

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#endif

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/* Get __GLIBC_FLT_EVAL_METHOD. */

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#include <bits/flt-eval-method.h>

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#ifdef __USE_ISOC99

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/* Define the following typedefs.

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float_t floating-point type at least as wide as `float' used

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to evaluate `float' expressions

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double_t floating-point type at least as wide as `double' used

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to evaluate `double' expressions

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*/

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# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16

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typedef float float_t;

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typedef double double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 1

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typedef double float_t;

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typedef double double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 2

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typedef long double float_t;

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typedef long double double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 32

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typedef _Float32 float_t;

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typedef double double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 33

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typedef _Float32x float_t;

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typedef _Float32x double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 64

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typedef _Float64 float_t;

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typedef _Float64 double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 65

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typedef _Float64x float_t;

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typedef _Float64x double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 128

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typedef _Float128 float_t;

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typedef _Float128 double_t;

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# elif __GLIBC_FLT_EVAL_METHOD == 129

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typedef _Float128x float_t;

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typedef _Float128x double_t;

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# else

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# error "Unknown __GLIBC_FLT_EVAL_METHOD"

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# endif

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#endif

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/* Define macros for the return values of ilogb and llogb, based on

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__FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.

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FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.

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FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.

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FP_LLOGB0 Expands to a value returned by `llogb (0.0)'.

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FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.

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*/

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#include <bits/fp-logb.h>

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#ifdef __USE_ISOC99

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# if __FP_LOGB0_IS_MIN

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# define FP_ILOGB0 (-2147483647 - 1)

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# else

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# define FP_ILOGB0 (-2147483647)

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# endif

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# if __FP_LOGBNAN_IS_MIN

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# define FP_ILOGBNAN (-2147483647 - 1)

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# else

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# define FP_ILOGBNAN 2147483647

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# endif

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#endif

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#if __GLIBC_USE (IEC_60559_BFP_EXT)

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# if __WORDSIZE == 32

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# define __FP_LONG_MAX 0x7fffffffL

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# else

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# define __FP_LONG_MAX 0x7fffffffffffffffL

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# endif

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# if __FP_LOGB0_IS_MIN

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# define FP_LLOGB0 (-__FP_LONG_MAX - 1)

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# else

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# define FP_LLOGB0 (-__FP_LONG_MAX)

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# endif

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# if __FP_LOGBNAN_IS_MIN

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# define FP_LLOGBNAN (-__FP_LONG_MAX - 1)

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# else

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# define FP_LLOGBNAN __FP_LONG_MAX

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# endif

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#endif

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/* Get the architecture specific values describing the floating-point

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evaluation. The following symbols will get defined:

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FP_FAST_FMA

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FP_FAST_FMAF

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FP_FAST_FMAL

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If defined it indicates that the `fma' function

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generally executes about as fast as a multiply and an add.

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This macro is defined only iff the `fma' function is

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implemented directly with a hardware multiply-add instructions.

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*/

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#include <bits/fp-fast.h>

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#if __GLIBC_USE (IEC_60559_BFP_EXT)

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/* Rounding direction macros for fromfp functions. */

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enum

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{

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FP_INT_UPWARD =

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# define FP_INT_UPWARD 0

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FP_INT_UPWARD,

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FP_INT_DOWNWARD =

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# define FP_INT_DOWNWARD 1

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FP_INT_DOWNWARD,

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FP_INT_TOWARDZERO =

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# define FP_INT_TOWARDZERO 2

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FP_INT_TOWARDZERO,

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FP_INT_TONEARESTFROMZERO =

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# define FP_INT_TONEARESTFROMZERO 3

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FP_INT_TONEARESTFROMZERO,

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FP_INT_TONEAREST =

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# define FP_INT_TONEAREST 4

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FP_INT_TONEAREST,

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};

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#endif

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/* The file <bits/mathcalls.h> contains the prototypes for all the

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actual math functions. These macros are used for those prototypes,

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so we can easily declare each function as both `name' and `__name',

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and can declare the float versions `namef' and `__namef'. */

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#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)

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#define __MATHCALL_VEC(function, suffix, args) \

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__SIMD_DECL (__MATH_PRECNAME (function, suffix)) \

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__MATHCALL (function, suffix, args)

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#define __MATHDECL_VEC(type, function,suffix, args) \

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__SIMD_DECL (__MATH_PRECNAME (function, suffix)) \

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__MATHDECL(type, function,suffix, args)

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#define __MATHCALL(function,suffix, args) \

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__MATHDECL (_Mdouble_,function,suffix, args)

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#define __MATHDECL(type, function,suffix, args) \

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__MATHDECL_1(type, function,suffix, args); \

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__MATHDECL_1(type, __CONCAT(__,function),suffix, args)

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#define __MATHCALLX(function,suffix, args, attrib) \

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__MATHDECLX (_Mdouble_,function,suffix, args, attrib)

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#define __MATHDECLX(type, function,suffix, args, attrib) \

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__MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \

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__MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)

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#define __MATHDECL_1(type, function,suffix, args) \

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extern type __MATH_PRECNAME(function,suffix) args __THROW

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#define _Mdouble_ double

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#define __MATH_PRECNAME(name,r) __CONCAT(name,r)

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#define __MATH_DECLARING_DOUBLE 1

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#define __MATH_DECLARING_FLOATN 0

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#include <bits/mathcalls-helper-functions.h>

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#include <bits/mathcalls.h>

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#undef _Mdouble_

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#undef __MATH_PRECNAME

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#undef __MATH_DECLARING_DOUBLE

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#undef __MATH_DECLARING_FLOATN

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#ifdef __USE_ISOC99

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/* Include the file of declarations again, this time using `float'

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instead of `double' and appending f to each function name. */

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# define _Mdouble_ float

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# define __MATH_PRECNAME(name,r) name##f##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 0

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# include <bits/mathcalls-helper-functions.h>

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# include <bits/mathcalls.h>

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \

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|| defined __LDBL_COMPAT \

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|| defined _LIBC_TEST

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# ifdef __LDBL_COMPAT

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# ifdef __USE_ISOC99

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extern float __nldbl_nexttowardf (float __x, long double __y)

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__THROW __attribute__ ((__const__));

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# ifdef __REDIRECT_NTH

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extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),

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__nldbl_nexttowardf)

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__attribute__ ((__const__));

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extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),

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nextafter) __attribute__ ((__const__));

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extern long double __REDIRECT_NTH (nexttowardl,

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(long double __x, long double __y),

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nextafter) __attribute__ ((__const__));

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# endif

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# endif

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# undef __MATHDECL_1

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# define __MATHDECL_2(type, function,suffix, args, alias) \

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extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \

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args, alias)

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# define __MATHDECL_1(type, function,suffix, args) \

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__MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))

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# endif

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/* Include the file of declarations again, this time using `long double'

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instead of `double' and appending l to each function name. */

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# define _Mdouble_ long double

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# define __MATH_PRECNAME(name,r) name##l##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 0

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# define __MATH_DECLARE_LDOUBLE 1

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# include <bits/mathcalls-helper-functions.h>

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# include <bits/mathcalls.h>

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */

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#endif /* Use ISO C99. */

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/* Include the file of declarations for _FloatN and _FloatNx

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types. */

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#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)

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# define _Mdouble_ _Float16

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# define __MATH_PRECNAME(name,r) name##f16##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT16

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC). */

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#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)

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# define _Mdouble_ _Float32

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# define __MATH_PRECNAME(name,r) name##f32##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT32

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC). */

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#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)

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# define _Mdouble_ _Float64

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# define __MATH_PRECNAME(name,r) name##f64##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT64

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC). */

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#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)

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# define _Mdouble_ _Float128

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# define __MATH_PRECNAME(name,r) name##f128##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT128

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC). */

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#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)

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# define _Mdouble_ _Float32x

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# define __MATH_PRECNAME(name,r) name##f32x##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT32X

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC). */

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[446] Fix | Delete

#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)

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# define _Mdouble_ _Float64x

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# define __MATH_PRECNAME(name,r) name##f64x##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT64X

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC). */

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[463] Fix | Delete

#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)

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# define _Mdouble_ _Float128x

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# define __MATH_PRECNAME(name,r) name##f128x##r

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# define __MATH_DECLARING_DOUBLE 0

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# define __MATH_DECLARING_FLOATN 1

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# if __HAVE_DISTINCT_FLOAT128X

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# include <bits/mathcalls-helper-functions.h>

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# endif

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# if __GLIBC_USE (IEC_60559_TYPES_EXT)

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# include <bits/mathcalls.h>

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# endif

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# undef _Mdouble_

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# undef __MATH_PRECNAME

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# undef __MATH_DECLARING_DOUBLE

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# undef __MATH_DECLARING_FLOATN

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#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC). */

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[480] Fix | Delete

#undef __MATHDECL_1

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#undef __MATHDECL

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#undef __MATHCALL

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[484] Fix | Delete

/* Declare functions returning a narrower type. */

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#define __MATHCALL_NARROW_ARGS_1 (_Marg_ __x)

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#define __MATHCALL_NARROW_ARGS_2 (_Marg_ __x, _Marg_ __y)

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#define __MATHCALL_NARROW_ARGS_3 (_Marg_ __x, _Marg_ __y, _Marg_ __z)

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#define __MATHCALL_NARROW_NORMAL(func, nargs) \

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extern _Mret_ func __MATHCALL_NARROW_ARGS_ ## nargs __THROW

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#define __MATHCALL_NARROW_REDIR(func, redir, nargs) \

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extern _Mret_ __REDIRECT_NTH (func, __MATHCALL_NARROW_ARGS_ ## nargs, \

[492] Fix | Delete

redir)

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#define __MATHCALL_NARROW(func, redir, nargs) \

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__MATHCALL_NARROW_NORMAL (func, nargs)

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#if __GLIBC_USE (IEC_60559_BFP_EXT)

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[498] Fix | Delete

# define _Mret_ float

[499] Fix | Delete